The Kremlin Wednesday expressed concern that tensions over Iran keep escalating despite assurances from US Secretary of State Mike Pompeo during a visit to Russia that Washington was not seeking war.

"So far we notice the continued escalation of tensions around this subject," Kremlin spokesman Dmitry Peskov said, a day after Pompeo met with President Vladimir Putin.

"We are saddened to see the decisions taken by the Iranian side," Peskov said, while arguing that Washington has been provoking Iran.

Speaking in the Black Sea resort city of Sochi on Tuesday, Pompeo assured Russia that his country did not want war with Iran, despite a spike in tensions that has seen the Pentagon dispatch nuclear-capable bombers to the region.

But Peskov sought to play down those statements.

"There were no assurances from Pompeo," Putin's spokesman told reporters.

"And one can hardly talk about some sort of assurances. There is an obvious situation which unfortunately tends to escalate further."

Washington last year pulled out of a nuclear deal backed by Europe, Russia and China, which curbed Iran's nuclear ambitions in return for sanctions relief.

Since then it has slapped sweeping sanctions on Iran in an all-out effort to reduce Tehran's regional clout.

On Sunday, mysterious attacks by unknown assailants against four ships in the region, including two from Saudi Arabia, sent war talk up another notch.

Washington has accused Iran of planning "imminent" attacks in the region and on Wednesday, the US ordered all non-emergency staff to leave its embassy in the Iraqi capital Baghdad and consulate in Arbil.